List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros)

Question

S(x) = 6x^4 − x^2 + 2x + 12

Answer 1

Any of the factors of 12 (1, 2, 3, 4, 6 and 12 itself) are to be considered as possible numerators (plus or minus), combined with any of the factors of 6 (1,2,3,6) as denominators, as representative of POSSIBLE rational zeros.

 

Thus, for example one half, one third, ...one sixth are possible rational zeros, as are their negatives.

 

Other examples include ±2/3  and  ±3/2